I just checked the Previous System Folder, Library. I don't have a Sounds folder
Sounds like you checked the HD/Library directory. Check the
Home/Library folder? You should have a Sounds folder. At least in 10.5.6 there is one. Your system info confirms you are still using 10.5.2. Have you considered updating?
I just checked the sounds in Mail Preferences and I do not have the swoosh sound listed as an option to choose. I listened to them all & none of them makes a swoosh sound. Perhaps that sound is not included in os 10.5.6.
If the swoosh sound is not in your Home directory, search the net for the swoosh sound (email sounds), install to your desktop, then move it to the Home directory sound folder.
Go to Mail Preferences/General, select New Mail Sound and from the drop down window select Add. Select your sound.
Repair permissions and restart your computer. Send some mail to yourself to make sure your mail alert is working properly.